Abelian PDSs have been extensively researched for decades, but research on non-abelian PDSs remains limited. Due to the fact that many techniques applicable to abelian groups cannot be directly applied to non-abelian cases, the study of non-abelian PDSs becomes challenging. In this paper, we use \(A_p(m,\theta )\) to represent the Suzuki p-groups of type A, which belong to a category of non-abelian p-groups. We combine tools from representation theory and character theory to explore these non-abelian groups, focusing on central PDSs, DSs, and linking systems. When the order of \(\theta \) is even, we establish some non-existence results for central PDSs in \(A_p(m, \theta )\) for p an odd prime and show that no non-trivial central DSs exist in \(A_2(m, \theta )\) . Additionally, when the order of \(\theta \) is odd, we construct some new infinite families of Latin square type central PDSs in \(A_p(m, \theta )\) applicable to any odd prime p; we construct central DSs and explore some (reduced) linking systems of DSs in \(A_2(m, \theta )\) .
